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An Introduction to the Ring Modulation Application

An Introduction to the Ring Modulation Application

AN INTRODUCTION TO THE RING APPLICATION

Changlong Li 460041137

Final Written Review for Systems, DESC9115, 2016 Graduate Program in Audio and Acoustics Faculty of Architecture, Design and Planning, University of Sydney

ABSTRACT 2. PROBLEM DESCRIPTION

This final written review introduces the brief history of ring 2.1. The Integration of Different Types of Ring Modulators modulation application and the basic modulation principle with a mathematical formula in introduction part. Then two potential The effect of the is still popular by the players problems are proposed, including the problem of the integration seeking for the sound with unique and metallic qualities of different types of ring modulators and the limitation of nowadays, so there are various types of ring modulator kits in the selectivity of inputs based on different durations of , market, such as the type with internal oscillator for generating which is solved by DSP and specified in specification part. By sinusoidal or rectangular carrier , the type only allowing using the demonstrated parameters and audio signals (saxophone self-modulation (which the both carrier signal and input signal and harp1), the whole script is implemented and the relevant are identical signals, or the input signal and delayed input signal) exported files have uploaded. Finally, two evaluation methods and so on. Therefore, it is worthwhile to design a well-designed (physical and performance evaluations) are proposed with all-in-one ring modulator kit to involve different types of ring diagrams. modulator kits by shifting the modes.

1. INTRODUCTION 2.2. The Limitation of Selectivity of Inputs Based On Different Durations of Signals Ring modulation (RM) regarded as a specific condition of (AM) has been applied in radio receivers Another problem is the limitation of selecting carrier signal, and extensively and was tried to be utilized in musical instruments the two inputs signals (original and carrier signals) cannot be from the late 1940s. The Melochord created by in ring-modulated arbitrarily because the multiplication between 1947 should be one of the earliest musical instruments using the two signals is based on the same signal duration (Orton, 2001). principle of ring modulation (Palov, 2011). Then Werner Meyer- From a different perspective, it will be significantly experimental Eppler used the Melochord broadly especially for electronic and endlessly possible to explore the effect of output ring- music (The "Melochord", 1949). With the popularization of the modulated signal providing that any two types of signals (such as ring modulator, that effect was applied by many audio projects. musical, noise, speech signal) can be set as the input signals. For example, the unique voice of the in the series (releasing from 1963 and produced by BBC Radiophonic 3. SPECIFICATION Workshop) could be regarded as one of the best-known ring modulation applications (Bentham, 1986).

The specification describes how the problems mentioned The electronic effect unit to implement the process of ring previously can be solved by digital . modulation is named ring modulator, which can multiply two signals (typically an input signal and a carrier signal) to generate a ring-modulated signal as the equation below (Orton, 2001). 3.1. The Specification for the Problem of the Integration of Different Types of Ring Modulators Sring-modulated(t) = Sinput(t) × Scarrier(t) There are four modes provided for users to select to meet the As for unique characteristics of the ring-modulated signal, there requirements of different users, namely pure tone inputs, a pure- are only the sum and subtraction of the inputs and tone carrier signal, self-modulation and unlimited inputs modes. both input and carrier signals are indistinctive in modulated The among the various modes is achieved by the signal (Burchardi, 2008). MATLAB if-elseif conditional statement. Moreover, users can select and implement their preferred mode by typing the corresponding mode name, which is fulfilled by MATLAB built- in functions input and strcmp.

1 The demonstrative audio files (saxophone and harp sounds) in this review are cited from the material lab of YiYing culture company.

In pure tone inputs mode, there are two sinusoidal waves as input delayed version of the input signal. The modulation process of and carrier signals to be ring modulated by the ringmodulation_ self-modulation mode can be achieved in ringmodulation_mode3 sinusoidal_wave.m. The specified procedures are illustrated by .m. diagram 1. Besides, at the end of each mode, the original, carrier and ring-modulated signal can be auditioned and exported by built-in functions sound and audiowrite.

Diagram 3. Procedures of the self-modulation mode (mode 3)

Diagram 1. Procedures of the pure tone inputs mode (mode 1) 3.2. The Specification for the Limitation of Selectivity of As for the pure-tone carrier signal mode, a sinusoidal or Inputs (Mode 4: Unlimited Inputs) rectangular wave can be selected (by built-in functions input and strcmp) as the carrier signal to modulate with an imported input Since the core principle of ring modulation is the multiplication signal (as the diagram 2). In case of the rectangular wave carrier of input and carrier signals in time domain, the signals’ durations signal, the function file ringmodulation_rectangular_wave.m is need to be identical. The basic approach for meeting the duration applied, whose principle is similar to ringmodulation_sinusoidal requirement is concatenating a piece of extra samples to the _wave.m but using built-in function square rather than a sin to shorter length input signal to let two signals have the same generate a rectangular wave. duration. Therefore, at the beginning of MATLAB function ringmodulation_mode4.m, the additional sample is calculated by the difference of two signals and created by built-in function zeros. Then the if-elseif conditional statement for comparing the lengths of two signals is applied to determine which signal should be concatenated with the extra samples. Diagram 4 illustrates the process of unlimited inputs mode.

Diagram 2. Procedures of the pure tone carriers signal mode (mode 2)

Diagram 3 illustrates the process of self-modulation mode. The name ‘self-modulation’ is because the carrier signal is the Diagram 4. Procedures of the unlimited inputs mode (mode 2)

4. IMPLEMENTATION

By running the script, a prompt message is displayed in the command window to ask which mode the user wants to use.

In mode 1 (code-lines 6-31)1, users are asked to set the sampling rate, signals’ duration, input signal and carrier signal Figure 1. The frequency of the ring-modulated signal is frequency. The values of 44100, 2, 200, and 600 are entered comprised by the add addition and subtraction of the input and respectively for implementation and demonstration purposes. carrier signals. Through the designed DSP, the input, carrier and ring-modulated signals are exported and named as ‘mode1_signal_input.wav’, 5.2. Performance Evaluation: The Recommended Ranges of ‘mode1_signal_carrier.wav’ and ‘mode1_signal_ringmodulated. Related Parameters wav’. The performance can be evaluated by the approach introduced in In mode 2 (code-lines 33-70), users need to preload the prepared lecture ‘Time-Variant Systems’ to test the variable factors of input signal and are asked to select whether the user wants to use different modes (University of Sydney, 2016). In mode 1, based the sinusoidal or rectangular as the carrier signal. The on predetermined sampling rate and durations, the description of corresponding carrier signal frequency needs to be typed in effect (such as fluctuated, , inharmonic, etc.) can be subsequently. In this review, a demonstrated saxophone sound is recorded in figure 2. preloaded as an input signal and the sinusoidal wave (300 Hz) is selected as a carrier signal. The exported files are ‘mode2_signal_carrier.wav’ and ‘mode2_signal_ringmodulated. wav’ for an audition.

In mode 3 (code-lines 72-86), in addition to the prepared input signal, the delay samples need to be entered for achieving the delay processing. The saxophone audio and delay sample (1000) are used for the implementation. The delayed signal and the ring- modulated signal are saved as ‘mode3_signal_carrier.wav’ and ‘mode3_signal_ringmodulated.wav’.

In mode 4 (code-lines 88-101), there are two audio signals to be prepared as the inputs of modulation function. The ring- modulated signal ‘mode4_signal_ringmodulated.wav’ is generated by the prepared saxophone and harp sounds in this Figure 2. The chart for evaluating the performance of mode 1 demonstration. The figure 3-5 illustrate the considered factors in x- and y-axis for evaluating the performance of mode 2-4 respectively. The 5. EVALUATION evaluation rate A-E is applied in indicating the degree from good (appropriate or usable effect) to bad (too much or little effect). The evaluation could be generalized by a large amount of users’ testing feedbacks. 5.1. Physical Evaluation: The Correctness of Ring Modulation Principle in the MATLAB Function

The correctness of ring modulation process can be verified by analyzing the plot of the ring-modulated signal in If the frequency is comprised by the add addition and subtraction of the input and carrier signals. The 200 and 600 Hz sinusoidal waves are used for verification. By adding the code- lines 39-60 in ringmodulation_sinusoidal_wave.m function and implementing the mode1, the figure 1 below is generated to verify the correctness.

1 All exported files, MATLAB scripts and functions are uploaded to the University of Sydney’s eScholarship Repository.

6. SUMMARY

This final written review introduces the brief history of ring modulation application and the basic modulation principle with a mathematical formula in introduction part. Then two potential problems are proposed, including the problem of the integration of different types of ring modulators and the limitation of selectivity of inputs based on different durations of signals, which is solved by DSP and specified in specification part. By using the demonstrated parameters and audio signals (saxophone and harp), the whole script is implemented and the relevant exported files have uploaded. Finally, two evaluation methods (physical and performance evaluations) are proposed with diagrams. With the further study on DSP and collecting feedbacks of users, the all-in-one ring modulator could be improved and developed to fit more users’ requirements.

Figure 3. The chart for evaluating the performance of mode 2 7. REFERENCES

[1] Burchardi, R. H. (2008, 9). Digital Simulation of the Ring Modulator for Musical. Proc. of the 11th Int. Conference on Digital Audio Effects (DAFx-08),. Finland. [2] Jeremy Bentham (1986), Doctor Who: The Early Years, p. 127, ISBN 0-491-03612-4 [3] Orton, R. (2001). Ring Modulator. In R. Orton, The New Grove Dictionary of Music and Musicians. London: Macmillan Publishers. [4] Rebekkah Palov (2011), "Harald Bode — A Short Biography", eContact! (Canadian Electroacoustic Community) 13 (4) [5] The "Melochord" (1947–9), The Keyboardmuseum Online, archived from the original on 2007-11-14 (description and history) [6] University of Sydney (2016) “Week 11 – Time variant systems” DESC9115 Digital Audio Systems [Lecture Content].

Figure 4. The chart for evaluating the performance of mode 3 8. LIST OF ILLUSTRATIONS

Diagram 1-4 are originally created by Changlong Li (the author of this review).

Figure 1. The frequency of the ring-modulated signal is comprised by the add addition and subtraction of the input and carrier signals. is created from MATLAB.

Figure 2-5 are originally created by Changlong Li (the author of this review).

Figure 5. The chart for evaluating the performance of mode 4

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